Why do some bones in my armature disappear when I go into Edit mode?
Unhide Bones

Your bones were hidden. To unhide them, once in Edit mode press ALTH and your bones will be back! 



Hidden Bones are only Hidden in Specific Modes

It is worth noting that bones hidden in one mode may be visible in another mode, and vice-versa. Here is an explanation from the Blender Manual:


  Note that hidden bones are specific to a mode – i.e. you can hide some
  bones in Edit mode, they will still be visible in Pose mode, and
  vice-versa. Hidden bone in Pose mode are also invisible in Object
  mode. And in Edit mode, the bone to hide must be fully selected, not
  just his root or tip…